A Note on Task-Aware Loss via Reweighing Prediction Loss by Decision-Regret

Understand

In this short technical note we propose a baseline for decision-aware learning for contextual linear optimization, which solves stochastic linear optimization when cost coefficients can be predicted based on context information.

• We propose a decision-aware version of predict-then-optimize.
• We reweigh the prediction error by the decision regret incurred by an (unweighted) pilot estimator of costs to obtain a decision-aware predictor, then optimize with cost predictions from the decision-aware predictor.
• This method can be motivated as a finite-difference, iterate-independent approximation of the gradients of previously proposed end-to-end learning algorithms; it is also consistent with previously suggested intuition for end-to-end learning.